Asked by Aimee michel on May 21, 2024
Verified
Use a graphing calculator to determine the number of real solutions of the quadratic equation 4x2−3x+9=04 x ^ { 2 } - 3 x + 9 = 04x2−3x+9=0 .
A) one real solution
B) no real solutions
C) two real solutions
Real Solutions
Solutions to equations that can be represented on the number line.
Graphing Calculator
A handheld calculator capable of plotting graphs, solving equations, and performing other complex mathematical tasks.
- Employ digital instruments (e.g., graphing calculators) to determine solutions or estimations.
Verified Answer
AW
Aytin WarsameMay 24, 2024
Final Answer :
B
Explanation :
Using the quadratic formula, we get
x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac
where $a=4$, $b=-3$, and $c=9$. Evaluating under the radical, we get
b2−4ac=(−3)2−4(4)(9)=−111<0b^2-4ac=(-3)^2-4(4)(9)=-111<0b2−4ac=(−3)2−4(4)(9)=−111<0
Since the discriminant is negative, there are no real solutions to the equation.
x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac
where $a=4$, $b=-3$, and $c=9$. Evaluating under the radical, we get
b2−4ac=(−3)2−4(4)(9)=−111<0b^2-4ac=(-3)^2-4(4)(9)=-111<0b2−4ac=(−3)2−4(4)(9)=−111<0
Since the discriminant is negative, there are no real solutions to the equation.
Learning Objectives
- Employ digital instruments (e.g., graphing calculators) to determine solutions or estimations.
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